Widgets have their own display repr which allows them to be displayed using IPython's display framework. Constructing and returning an IntSlider automatically displays the widget (as seen below). Widgets are displayed inside the widget area, which sits between the code cell and output. You can hide all of the widgets in the widget area by clicking the grey x in the margin.

Widgets are represented in the back-end by a single object. Each time a widget is displayed, a new representation of that same object is created in the front-end. These representations are called views.

If you need to display the same value two different ways, you'll have to use two different widgets. Instead of attempting to manually synchronize the values of the two widgets, you can use the traitletlink function to link two properties together. Below, the values of three widgets are linked together.